1. Field of Invention
The present invention relates to a new type of so-called energy-trapping-type surface acoustic wave resonator (hereinafter “SAW resonator”), formed on a piezoelectric plate, such as a quartz crystal, in which vibration energy is greatly concentrated in the center of the resonator so as to increase the Q value and reduce the CI value by using a Rayleigh-type or STW (surface Transverse wave) type surface acoustic wave.
2. Description of Related Art
A related art SAW resonator, formed by using a quartz-crystal ST-cut substrate (an example of a piezoelectric plate) having piezoelectricity, can be used as an oscillation device of a quartz-crystal oscillator for data transmission in various high-speed network systems because the frequency-temperature characteristics thereof have a zero temperature coefficient and have excellent accuracy. This is advantageous in that a signal without jitter and whose phase noise is reduced can be obtained with high accuracy and at a low cost.
However, in the related art, the signal transmission speed of network systems has increased up to the GHz band, and a demand exists for higher-accuracy quartz-crystal oscillators. In connection with the above, a related art SAW resonator disclosed in Japanese Patent Application Publication No. 57-73513 uses a rotated ST-cut quartz-crystal plate, and approximately half of frequency-temperature characteristics (accuracy ±50 ppm) is obtained with respect to the accuracy ±100 ppm (in the range of 0 to 70° C.) of the above-described ST cut plate. The above-mentioned substrate uses a Rayleigh-type surface acoustic wave.
Regarding such a rotated ST-cut quartz-crystal plate (hereinafter “R-ST substrate” from “rotated ST cut substrate”), the orientations thereof are shown in FIG. 13. In FIG. 13, reference numeral 1302 denotes the electrical axis X, which is a fundamental axis of a quartz crystal, reference numeral 1303 denotes the mechanical axis Y, and reference numeral 1304 denotes the optical axis Z. For the R-ST substrate, in a substrate 1300 such that a Y plate indicated by 1301 is rotated by θ degrees (in particular, θ=31 to 42 degrees, at which a zero temperature coefficient is obtained) about the electrical axis X, a rotational angle Ψ=±(40 to 46) degrees within the plane from the electrical axis X (=y axis of the device) in the substrate (1300 and 1307 are the same) is the phase propagation orientation (X′=the x axis of the device) of the surface acoustic wave used.
A SAW resonator 1306 using a R-ST substrate is formed along the x axis, as shown in FIG. 5 (described below). An interdigital transducer (hereinafter “IDT”), in which electrode fingers of many parallel conductors made of, for example, aluminum metal are arranged periodically, is formed, and a pair of reflectors are formed by arranging many electrode conductors in a strip shape in parallel and periodically, thereby forming a one-port-type SAW resonator.
More specifically, for example, in a related art SAW resonator in a related art ST cut plate (θ=31 to 42 degrees, and the phase propagation direction of the surface acoustic wave is the electrical axis (X axis)), as an essential point when the IDT is formed, when M pairs are formed by assuming a positive electrode and a negative electrode to be one pair, after the total reflection coefficient Γ of all electrode fingers of the IDT is defined as shown in the following equation (1), if Γ is set such that 10>Γ>0.8, a so-called energy-trapping-type SAW resonator discussed in Technical Report of the IEICE US87-36, pp 9-16 (1987.9), in which the vibration energy is concentrated in the center of the resonator, can be realized.
[Equation 1]Γ=4MbH/λ  (1)where M is the number of pairs in the IDT, b is the reflection coefficient rate of the surface acoustic wave per electrode, H is the film thickness of the conductor, and λ is the wavelength of the surface acoustic wave used.
For example, in the case of the IDT formed of the above-mentioned aluminum conductor in the ST-cut quartz-crystal plate, if M=80 pairs with b=0.255 and H/λ=0.03 (3%), a related art one-port-type SAW resonator having satisfactory Q and CI characteristics can be formed. At this time, Γ is approximately 2.448 degrees. the generally called reflection coefficient γ per electrode is γ=b(H/λ)=Γ/(4M)=0.00765 (0.76%) on the basis of equation (1) described above in the case of this ST-cut quartz-crystal plate.
When the state of the vibration displacement of the energy-trapping-type surface acoustic wave resonator is calculated by a related art calculation technique, it is found that the vibration displacement is in the state shown in FIG. 2. The vibration displacement refers to an envelope amplitude U(x) such that the maximum values of the vibration displacements which steadily vibrate periodically with time are connected (201 in FIG. 2). In FIG. 2, the horizontal axis shows the position coordinate of the center position (node) of the line width formed by one electrode of the SAW resonator formed of two reflectors on the two sides and the IDT. Regarding the vertical axis, the left side shows the relative value of U(x) and the right side shows the value of N(x)=U(x)/Umax, that is, the U(x) normalized by Umax=3.3, which is the maximum value of U(x). The coordinate from 0 to 1, shown in the upper portion of FIG. 2, is a coordinate value in which the position coordinate of the IDT is normalized across the total length of the IDT, with one of the ends being set at 0 and the other end being set at 1. The normalized amplitude N(x) in a related art SAW resonator is a smooth function in the form of a cosine function which takes N(x)=1 at ½ (the center position of the IDT region) of the total length, which takes 0.78 at ¼ and ¾, and which takes a value of 0.30 at both ends 0 and 1 of the IDT. The form of this function is called a “standard-type” by setting this function as NO(x) for later discussion.
Idea-related analysis results in which the degree of energy concentration at the center is increased more than NO(x) are disclosed in Japanese Patent Application Publication No. 10-335966, which is a document of the inventors of the present invention. However, in that publication, those analysis results are not yet described as a detailed and practical specific example in which they are quantized.